On Semiclean Group Rings
Received:December 07, 2015  Revised:December 02, 2016
Key Word: clean ring   semiclean ring   group ring   locally finite group  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11401009) and the Natural Science Foundation of Ahui Province (Grant No.1408085QA01).
Author NameAffiliation
Xianmei SONG Department of Mathematics, Anhui Normal University, Anhui 241000, P. R. China 
Yuxia MEI Department of Mathematics, Anhui Normal University, Anhui 241000, P. R. China 
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Abstract:
      A ring $R$ with unity is called semiclean, if each of its elements is the sum of a unit and a periodic. Every clean ring is semiclean. It is not easy to characterize a semiclean group ring in general. Our purpose is to consider the following question: If $G$ is a locally finite group or a cyclic group of order 3, then when is $RG$ semiclean? Some known results on clean group rings are generalized.
Citation:
DOI:10.3770/j.issn:2095-2651.2017.02.007
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